An incendiary remark by Rick Santorum’s biggest financial backer illustrates one of the key dangers posed by a new breed of outside political groups: their ability to cause problems for the candidates they’re trying to help.

Foster Friess, a millionaire Wyoming investor bankrolling a pro-Santorum group, caused an uproar this week by wading into the contraception debate with a quip about women’s sexuality.

“You know, back in my days, they’d use Bayer aspirin for contraceptives,” Friess said on MSNBC. “The gals put it between their knees, and it wasn’t that costly.”

The remark outraged women’s groups and many others, quickly becoming a distraction for Santorum as he attempts to build on a trio of victories that threaten rival Mitt Romney.

“When you quote a supporter of mine who tells a bad off-color joke and somehow I am responsible for that, that is ‘gotcha,’ ” he said.

But political strategists and campaign finance experts say candidates have little choice but to deal with the fallout from actions taken by their supporters, even if they are ostensibly independent from the campaigns. Many of the biggest financiers of super PACs are part of a new breed of “super bundlers” who also contribute to, or raise money for, their favored candidate’s campaign.

“The fact that Santorum is spending so much time discussing what his super PAC contributor said suggests he understands very well how important the group is to his campaign,” said Ellen Miller, executive director of the Sunlight Foundation watchdog group. “He has to talk about it.”

Presidential candidates have waffled in their approaches to super PACs and other outside groups, attempting to maintain their distance while also taking advantage of the clear financial benefits they offer.

President Obama, who has long decried the role of special-interest money in politics, decided last week to encourage fundraising by a pro-Democratic super PAC in the face of strong fundraising by such groups on the other side. Romney, who had already appeared at fundraisers for a super PAC, signaled he would do the same.

All the major presidential candidates have a super PAC dedicated to their cause, funded heavily by billionaire financiers, hedge fund managers and corporate tycoons writing six- and seven-figure checks. The groups emerged from court rulings allowing corporations, unions and individuals to spend and raise unlimited amounts of money in elections as long as they do not directly coordinate with candidates.

This close-but-not-too-close relationship has put several candidates on the spot, particularly when it comes to the sharp-edged attack ads that flooded the airwaves in early primary states.

In January, for example, former House speaker Newt Gingrich sought to distance himself from a series of ads, attacking Romney as a former corporate raider, that were funded by Winning Our Future, a pro-Gingrich super PAC funded by $11 million in contributions from a Las Vegas casino magnate and his family.

Gingrich and Romney traded jabs on the issue during a debate in South Carolina. Gingrich said Romney’s claims that he had no control over a pro-Romney super PAC called Restore Our Future “makes you wonder how much influence he’d have if he were president.”

Romney responded: “I already said at our last debate that anything that’s false in PAC ads, whether they are supportive of me or supportive of you, should be taken off the air and fixed. I’ve already said that.”

Santorum, a deeply conservative Catholic, has blasted the administration’s policy while also coming under fire from Democrats for previous comments condemning contraception as a sin. The candidate seemed to bristle at the idea that Friess’s aspirin remark should be tied to him, while also defending his benefactor’s character and intent.

“Foster is known in political circles as telling a lot of jokes, and some of them are not particularly funny, which this one was not. He’s not creepy. He’s a good man,” Santorum said Thursday night on Fox News. “You know, he told a bad, off-color joke, and he shouldn’t have done it. . . . It was a stupid joke.”

Friess also apologized for his remark on his personal blog: “To all those who took my joke as modern day approach I deeply apologize and seek your forgiveness. My wife constantly tells me I need new material — she understood the joke but didn’t like it anyway — so I will keep that old one in the past where it belongs.”

Friess gave more than $300,000 in 2011 to a pro-Santorum super PAC called the Red, White and Blue Fund; he has acknowledged giving more in 2012 that has yet to be reported in disclosure forms. The super PAC has spent at least $1.2 million on Santorum’s behalf, according to tracking data, and the group announced it would spent $700,000 more on ads in Michigan ahead of the Feb. 28 primary.

Friess has also given $2,500 to Santorum’s primary campaign and is a longtime donor to the Republican Governor’s Association and other GOP causes, Federal Election Commission records show.

Paul S. Ryan, associate counsel at the Campaign Legal Center in Washington, said that although the Friess aspirin remark causes headaches for Santorum’s campaign, “the real risk posed by mega-funders is to voters and our political system.”

“Candidates are now beholden to mega-funders in a way that, at a minimum, creates an appearance of corruption and may lead to actual corruption,” Ryan said. “Elected officials will likely do the bidding of their mega-funders while in office, rather than acting in the public interest, knowing that they’ll need to rely on such mega-funders for reelection.”